contradictory anti-housing arguments

Over the years, I’ve heard a wide variety of arguments against new housing. One of them is the “mysterious foreign investor” argument. According to this theory, new urban housing will all be bought up by billionaire foreign investors, who will purchase the property and never rent it out, thus preventing the new housing from increasing supply. (I have rebutted the argument here).* A variation of the argument is that because some high-end housing is vacant, supply is therefore adequate to meet demand. (I have addressed this idea here). Another argument is that housing markets are segmented: that if you increase the supply at the top of the market, it will not help anyone who is not already at the top of the market. It seems to me that these arguments contradict each other: the first argument is based on the idea that high-end housing does affect the market as a whole (or would if rich people stopped using apartments as second homes); the second is based on the idea that high-end housing doesn’t affect the rest of the market at all. *In addition, I have recently published a much longer article in the New Mexico Law Review, discussing the pros and cons of high-end condos.